Senate officials were told about the loans but not federal election authorities

WASHINGTON—Texas Sen. Ted Cruz didn’t disclose to election officials a pair of loans he took from Wall Street banks when he first ran for the Senate in 2012, an omission that could violate campaign rules.

Mr. Cruz, a Republican, helped pay for his 2012 election campaign in part by taking out personal loans from Citigroup Inc. and Goldman Sachs Group Inc. that were eventually worth a total of between $500,001 and $1 million, according to financial disclosure forms that he filed with the Senate. Mr. Cruz’s wife, Heidi,...